Storing self-inflating mattresses

We have just returned from 3 weeks desert camping on our new 100mm thick self-inflating mattresses. Very comfortable and worth every cent.

For long term storage and to maximise their life, will they lose their spring if we keep them rolled up and tied? My gut feeling is that they would last better if left inflated - we could store them at home under a bed.

I would appreciate any views or experiences.

Thanks, Gado